The Centers for Disease Control and Prevention (CDC) is required by law to publish a report on assisted reproductive technologies (ART). ART includes all fertility treatments in which both the egg and the sperm are used. These procedures generally involve removing eggs from a woman’s ovaries, combining them with sperm in the laboratory, and returning them to the woman’s body or giving them to another woman.
You are helping to prepare the CDC report and select at random 10 ART cycles for a special review. None of the cycles resulted in a clinical pregnancy. Your manager feels it is impossible to select at random 10 ART cycles that did not result in a clinical pregnancy. Use the information in the diagrams on the last page and your knowledge of statistics to determine if your manager is correct.
As preparation to assemble your final report, consider:
a. How would you determine if your manager’s view is correct, that it is impossible to select at random 10 ART cycles that did not result in a clinical pregnancy?
b. What probability distribution do you think best describes the situation? Do you think the distribution of the number of clinical pregnancies is discrete or continuous? Why?
* With these answers in mind,
● Write an explanation that answers the question, “Is it possible to select at random 10 ART cycles that did not result in a clinical pregnancy?” Include in your explanation the appropriate probability distribution, your calculation of the probability of no clinical pregnancies in 10 ART cycles, AND a full probability histogram which depicts the probabilities for all possible values of the random variable in this experiment.
● What is the “expected value” of clinical pregnancies from a random sampling of 10 ART cycles?
As follow-up to your final report, consider:
Which of the following samples would you consider suspicious if someone told you that the sample was selected at random? Would you believe that the samples were selected at random? Why or why not?
a. Selecting at random 10 ART cycles among women of age 40, eight of which resulted in clinical pregnancies.
b. Selecting at random 10 ART cycles among women of age 41, none of which resulted in clinical pregnancies.
● Answer to Preparation Questions
● Answers to Research Questions
○ Probability Histogram (can be computer-generated; if hand-drawn, must be on graph paper)
● Answers to Follow-Up Questions
● Work + Calculations (may be handwritten NEATLY